Oriented Triplet $p$-Wave Pairing from Fermi surface Anisotropy and Nonlocal Attraction

Using constrained-path quantum Monte Carlo, we map the ground-state phase diagram versus the nearest-neighbor (NN) attraction $V$ and spin-dependent hopping anisotropy $\alpha$ for the two-dimensional attractive $t$–$U$–$V$ Hubbard model at filling $n\simeq 0.85$. We identify an onsite $s$-wave superfluid, a Cooper pair Bose metal with an uncondensed Bose surface, and an oriented equal-spin triplet $p$-wave pairing phase. The NN attraction activates the odd-parity channel, while hopping anisotropy suppresses the competing $s$-wave coherence and selects a $p_x\mathrm{/}{p}_y$ polar axis, and thus lowers the critical $\mathrm{\mid }{V}_c\mathrm{\mid }$ for the onset of triplet-dominant $p$-wave pairing. A channel-resolved Landau analysis provides a criterion for the Landau $p$-wave scale $V_c^{\mathrm{L}}(\alpha )$, consistent with the observed anisotropy dependence of $\mathrm{\mid }{V}_c\mathrm{\mid }$. Our results establish how NN interaction and Fermi surface anisotropy cooperate to generate the oriented triplet $p$-wave pairing, and suggest that cold-atom and altermagnetic platforms could potentially realize this mechanism.